(1) Field of the Invention
The present invention relates to a control method and a drive circuit for a polarization scrambler which changes the state of polarization of incident light with time.
(2) Description of the Related Art
When transmission factors for optical components are measured, a light source for measurement, such as a semiconductor laser, a light-emitting diode (LED), a super luminescent diode (SLD), etc., is generally employed. Such a light source usually emits linearly polarized light. Therefore, in the case where measurements must be made in a state of non-polarization, linearly polarized light is caused to be in a state of non-polarization by a polarization scrambler.
Existing polarization scramblers are constructed mainly of birefringent materials. Examples of birefringent materials are an electro-optical crystal such as LN, (Pb,La) (Zr,Ti)O3 (hereinafter referred to as PLZT), etc., a liquid crystal, an optical fiber, etc. As shown in FIG. 8, for example, the optic axis 101 of a birefringent material 100 is basically disposed within a plane perpendicular to a direction in which incident light propagates. In the case where incident light is linearly polarized light, the optic axis 100 is disposed to form an angle of 45 degrees with the direction of polarization.
Light incident on the birefringent material 100 is divided into ordinary light and extraordinary light, which propagate through the birefringent material 100. At the exit end of the birefringent material 100, the ordinary light and the extraordinary light are synthesized with a phase difference Δφ represented by the following Eq. (1):Δφ=(2π/λ)·Δn·L  (1)where Δn is the refractive index difference between ordinary light and extraordinary light, L is the length of the birefringent material 100, and λ is the wavelength of incident light.
If a predetermined driving voltage waveform is applied across the birefringent material 100, a change in the refractive index difference Δn occurs by an electric-optical effect (when the birefringent material 100 is LN or PLZT), or by rotation of a liquid crystal molecule (when the birefringent material 100 is a liquid crystal), or by an photo-elastic effect (when the birefringent material 100 is an optical fiber) which is obtained by deforming an optical fiber with a piezoelectric element, etc.
With an increase in the refractive index difference Δn, the polarization state of the synthesized light changes in the order of linear polarization→circular polarization→diagonal linear polarization→reverse circular polarization→original linear polarization. Note that a Faraday rotator is often utilized instead of the birefringent material 100. In this case, a driving current waveform is applied across the Faraday rotor, and incident light with linear polarization is rotated by a Faraday effect while holding the linear polarization. The relation of a driving voltage waveform to the birefringent material 100 is the same as the relation of a driving current waveform to a Faraday rotor.
The light synthesized as described above is instantaneously in a certain polarization state, and is not in a non-polarization state. However, if the cycle of a driving voltage waveform is made sufficiently shorter than a response time or sampling cycle for measurement, then the result of measurement will be the same as the result of measurement in a non-polarization state. That is, a measuring system is in a non-polarization state. Under such a principle, polarization scramblers operate.
Note that the definition of the degree of polarization (DOP) is given by the following Eq. (2):DOP=(S12+S22+S32)1/2/S0  (2)where S0, S1, S2, and S3 are Stokes parameters.
The Stokes parameter represents the state of polarization averaged at a certain time. When the DOP is considered as described above, the Stokes parameter is a value averaged in the cycle of a driving voltage waveform that is sufficiently shorter than a sampling cycle for measurement. The Stokes parameter (vector) in this state will hereinafter be referred to as an average Stokes parameter (vector).
To represent an instantaneous polarization state, consider instantaneous polarization as a Stokes parameter (vector) averaged in a sufficiently shorter time than the cycle of a driving voltage waveform. In the case of FIG. 9, for example, instantaneous polarization is present on a longitude line that is a line of intersection between plane S2=0 and the Poincare sphere. If a driving voltage waveform is applied across a polarization scrambler (phase shifter), the state of polarization represented on the longitude line will change. Note that the position corresponding to the north pole of the Poincare sphere represents circularly polarized light. The position corresponding to the south pole represents left-circularly polarized light, the position corresponding to the equator represents linearly polarized light, and other positions represent elliptically polarized light.
If the amplitude of a driving voltage waveform is adjusted so that the aforementioned phase difference Δφ represented by Eq. (1) is exactly 0 to 2π at a certain wavelength λ0, and a change in the refractive index difference Δn, that is, a driving voltage waveform is selected so that instantaneous polarization is present uniformly on the longitude line within the cycle of the driving voltage waveform, then S12+S32 will approach zero and the DOP will approach zero. That is, linearly polarized light is caused to in a state of non-polarization. On the other hand, in the case where no driving voltage waveform is applied, S12+S32 equals S02 in average and instantaneously, and the DOP becomes 1. That is, linearly polarized light is caused to be in a complete polarization state.
As an example, the construction of a polarization scrambler employing LN is shown in FIG. 10, a driving voltage waveform is shown in FIG. 11, and a state of polarization is represented by a locus on the Poincare sphere in FIG. 12.
As shown in FIG. 10, the polarization scrambler includes an input fiber 201, an input lens 202, an LN element 203, an output lens 204, and an output fiber 205. The LN element 203 is equipped with a waveguide 206. Electrodes 207 and 208 are formed around and near the waveguide 206.
The driving voltage waveform shown in FIG. 11 is applied between the electrodes 207 and 208, and the amplitude is adjusted so that the aforementioned phase difference Δφ is exactly 0 to 2π at a certain wavelength λ0. In addition, since the refractive index difference Δn is approximately proportional to the amplitude of a driving voltage, a waveform that varies linearly (e.g., a triangular waveform shown in FIG. 11) is employed so that instantaneous polarization is distributed uniformly on a longitude line of the Poincare sphere within the cycle of a driving voltage waveform. However, in the case of a polarization scrambler employing LN, it is known that if a driving voltage waveform has a DC component, the characteristics of LN will change. For this reason, a driving voltage waveform having no DC component is usually used.
If such a triangular waveform is applied as a driving voltage waveform for a polarization scrambler, instantaneous polarization changes along a longitude line (heavy solid line) of the Poincare sphere shown in FIG. 12, as described below. The points A and B on the longitude line of the Poincare sphere correspond to the points A and B on the triangular waveform shown in FIG. 11, respectively.
Initially, in the section AB of the triangular waveform of FIG. 11 in which the voltage increases, instantaneous polarization starts from the point A, changes along the longitude line (heavy solid line) of the Poincare sphere of FIG. 12 in the direction indicated by an arrow (A→B), and reaches the point B (which is coincident with the point A).
In the section BA of the triangular waveform of FIG. 11 in which the voltage decreases, instantaneous polarization starts from the point B in the opposite direction and returns to the point A. Each time an increase and decrease in the driving voltage waveform is repeated in this way, instantaneous polarization changes repeatedly along the longitude line (heavy solid line) of the Poincare sphere with the point A (point B) as the starting point and end point.
Therefore, in this case, instantaneous polarization is distributed uniformly on the longitude line (heavy solid line) of the Poincare sphere. Thus, it is understood that the DOP calculated by average Stokes vectors is ideally zero.
For a more detailed discussion on the operation of polarization scramblers employing LN, see, for example, F. Heisman, “Compact Electro-Optic Polarization Scramblers for Optically Amplified Lightwave Systems,” IEEE Journal of Lightwave Technology Vol. 14, No. 8 1801 (1996). In the case of polarization scramblers employing birefringent materials other than LN, a driving voltage waveform in which the voltage changes linearly, such as a triangular waveform, is not always optimum. That is, it is necessary to select a driving voltage waveform which can change a refractive index difference Δn so that Stokes vectors (state of polarization) are distributed uniformly on the longitude line of the Poincare sphere within the cycle of the driving voltage waveform.
In the case where transmission factors for optical components are measured by a light source (such as a semiconductor laser, an LED, a SLD, etc.), a polarization scrambler, and an optical spectrum analyzer, measurements are made in a wide wavelength range by the optical spectrum analyzer and therefore the DOP must be small in the wide wavelength range. For instance, considering measurements are made in S, C, and L bands that are used for optical communication, the DOP has to be small in a wide range of 1450 to 1620 nm.
However, as previously described, the amplitude of a driving voltage waveform is adjusted so that the phase difference Δφ is exactly 0 to 2π at a certain wavelength λ0. Because of this, if the wavelength λ of incident light to be scrambled is shifted form the wavelength λ0, the phase difference Δφ will change in inverse proportion to the wavelength λ. For example, if the wavelength λ becomes smaller than the wavelength λ0, the phase difference Δφ will increase in inverse proportion to the wavelength λ. As a result, the maximum value of the phase difference Δφ becomes greater than 2π, instantaneous polarization is no longer uniformly distributed on the longitude line of the Poincare sphere, and the DOP increases.
The locus of the instantaneous polarization at this time is shown in FIG. 13. The points A′ and B′ on a longitude line (heavy solid line) of the Poincare sphere shown in the figure correspond to the points A and B on the driving voltage waveform (triangular waveform) shown in FIG. 11, respectively. As shown in FIG. 13, instantaneous polarization starts from the point A′ on the longitude line and changes in the direction indicated by an arrow. Since the maximum value of the phase difference Δφ becomes greater than 2π, instantaneous polarization reaches the point B′ (which is longer than the length around the longitude line) beyond the point A′. Thereafter, instantaneous polarization changes in the opposite direction from the point B′ and returns to the point A′.
That is, in this case, the locus of instantaneous polarization is repeated over the arc A′B′ of the Poincare sphere, so instantaneous polarization is not uniformly distributed and DOP increases. The same is also true of polarization scramblers employing birefringent materials other than LN, and driving voltage waveforms different in shape from the above-described triangular waveform.
A DOP for the polarization scrambler shown in FIG. 10 is given as a function of wavelength λ by the following Eq. (3):DOP=2×|sin(2πλ0/λ)|/(2πλ0/λ)  (3)
FIG. 14 shows values calculated by Eq. (3) and measured values. As shown in the figure, it is understood that the calculated values are well coincident with the measured values and that DOP can be sufficiently evaluated from the calculated values. In this case, the amplitude of a driving voltage waveform is adjusted so that the aforementioned phase difference Δφ is exactly 0 to 2 π at a wavelength of λ0=1560 nm, that is, so that DOP has a minimum at a wavelength of λ0=1560 nm. It is also understood that if the wavelength λ of incident light is shifted from λ0=1560 nm, DOP increases linearly and that DOP rises up to about 11% at wavelength λ=1470 nm.
Considering measurements are made in S, C, and L bands that are used for optical communication, it is preferable to set λ0 to 1530 nm which is the center between 1450 nm and 1620 nm. However, in the case of wavelength λ=1450 nm (or λ=1620 nm), DOP calculated by Eq. (3) is about 11% and has a bad effect on measurement.
Thus, in the case of the polarization scrambler employing the conventional driving voltage waveform, the DOP is great in a wide wavelength range, for example, a range of 1450 to 1620 nm which is S, C, and L bands for optical communication, and has a bad effect on measurement. As a result, the conventional polarization scrambler cannot be used as a polarization scrambler for a measurement light source.